A general Fourier solution for the vibration analysis of composite laminated structure elements of revolution with general elastic restraints

Abstract A unified modified Fourier solution based on the first order shear deformation theory is developed for the vibrations of various composite laminated structure elements of revolution with general elastic restraints including cylindrical, conical, spherical shells and annular plates. Regardless of boundary conditions, each displacement and rotation component of the structures is invariantly expressed as the superposition of a Fourier cosine series and two supplementary functions introduced to remove any potential discontinuous of the original displacements and their derivatives. On the basis of energy functional of structure elements, the exact series solutions are obtained using the Rayleigh–Ritz procedure. The accuracy and convergence of the proposed modified Fourier series solution are demonstrated by the comprehensive numerical examples. A variety of new vibration results including frequencies and mode shapes for composite laminated cylindrical, conical, spherical shells and annular plates with classical and elastic restraints as well as different geometric and material parameters are presented, which may serve as benchmark solution for future researches. The effects of the elastic restraint parameters, layout orientations, number of layers, conical angles and degrees of anisotropic on the vibration frequencies of the structures are illustrated.